scholarly journals Nonlinear Static Bending and Free Vibration Analysis of Bidirectional Functionally Graded Material Plates

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Nguyen Thi Hong
Keyword(s):  
Free Vibration ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Third Order ◽  
Aspect Ratios ◽  
Graded Material ◽  
Nonlinear Static

Bidirectional functionally graded material (2D-FGM) plates have mechanical properties that vary continuously in both the thickness and one-edge directions; these plates are more and more widely used in design and engineering applications. When these structures are subjected to strong loads, they can be largely deformed; therefore, nonlinear calculations, in this case, are necessary. In this paper, nonlinear static bending and nonlinear free vibration behaviors of 2D-FGM plates are studied by using the finite element method based on the third-order shear deformation theory; the Newton-Raphson method is used to solve this problem. The accuracy of this approach is confirmed by comparing the results with respect to other papers. The effects of some numerical aspect ratios such as volume fraction index and thickness-to-length ratio on nonlinear static bending and free vibration of the plates are explored. This study shows that there is a big difference between the numerical results obtained from the nonlinear problem and those from the linear one.

Free vibration analysis of rotating functionally graded material plate under nonlinear thermal environment using higher order shear deformation theory

2018 ◽  
Vol 233 (6) ◽  
pp. 2056-2073 ◽  
Author(s):  
S Parida ◽  
SC Mohanty
Keyword(s):  
Free Vibration ◽  
Functionally Graded Material ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Graded Material

In the present article, a higher order shear deformation theory is used to develop a finite element model for the free vibration analysis of a rotating functionally graded material plate in the thermal environment. The model is based on an eight-noded isoparametric element with seven degrees-of-freedom per node. The material properties are temperature dependent and graded along its thickness according to a simple power law distribution in terms of volume fraction of the constituents. The general displacement equation provides C0 continuity, and the transverse shear strain undergoes parabolic variation through the thickness of the plate. Therefore, the shear correction factor is not used in this theory. The obtained results are compared with the published results in the literature to determine the accuracy of the method. The effects of various parameters like hub radius, rotation speed, aspect ratio, thickness ratio, volume fraction index, and temperature on the frequency of rotating plate are investigated.

Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects

2020 ◽  
Vol 234 (18) ◽  
pp. 3667-3688
Author(s):  
Ismail Bensaid ◽  
Ahmed Amine Daikh ◽  
Ahmed Drai
Keyword(s):  
Free Vibration ◽  
Power Law ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Size Dependent ◽  
Graded Material

The investigation conducted in this paper aims to study free vibration and buckling behaviors of size-dependent functionally graded sandwich nanobeams. In order to take into account the small size effects, nonlocal elasticity theory of Eringen's is incorporated. Material properties of the functionally graded sandwich beams are supposed to change continuously through the thickness direction according to two forms of the volume fraction of constituents by power law functionally graded material and sigmoid law functionally graded material. These rules are modified to consider the effect of porosity, which covers four kinds of porosity distributions. Two types of sandwich nanobeams were provided: (a) homogeneous core and functionally graded skins and (b) functionally graded core and homogeneous skins. Third-order shear deformation theory without any shear correction factor in conjunction with Hamilton's principle is used to extract the governing equations of motions of porous functionally graded sandwich nanobeams and then solved analytically for two hinged ends. The effects of nonlocal parameter, length to thickness ratios, material graduation index, amount of porosity, porosity distribution shape, on the nondimensional frequency and critical buckling load of the functionally graded sandwich nanobeams made of porous materials are exhibited by a parametric study.

TSDT theory for free vibration of functionally graded plates with various material properties

2021 ◽  
Vol 8 (4) ◽  
pp. 691-704
Author(s):  
M. Janane Allah ◽  
◽  
Y. Belaasilia ◽  
A. Timesli ◽  
A. El Haouzi ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Implicit Algorithm ◽  
Proposed Model ◽  
Graded Material ◽  
Composite Modeling

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

A third-order shear deformation theory for nonlinear vibration analysis of stiffened functionally graded material sandwich doubly curved shallow shells with four material models

2017 ◽  
Vol 21 (4) ◽  
pp. 1316-1356 ◽  
Author(s):  
Dang T Dong ◽  
Dao Van Dung
Keyword(s):  
Functionally Graded Material ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Shallow Shells ◽  
Graded Material ◽  
Doubly Curved

This study presents a nonlinear vibration analysis of function graded sandwich doubly curved shallow shells, which reinforced by functionally graded material stiffeners and rested on the Pasternak foundation. The shells are subjected to the combination of mechanical, thermal, and damping loading. Four models of the sandwich shells with general sigmoid and power laws distribution are considered. The governing equations are established based on the third-order shear deformation theory. Von Kármán-type nonlinearity and smeared stiffener technique are taken into account. The explicit expressions for determining natural frequencies, nonlinear frequency–amplitude relation, and time–deflection curves are obtained by employing the Galerkin method. Finally, the fourth-order Runge–Kutta method is applied to investigate the influences of functionally graded material stiffeners, the boundary conditions, the models of the shells, thermal environment, foundation and geometrical parameters on the natural frequencies and dynamic nonlinear responses of the sandwich shells.

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